Question

2. (11 points) It is recommended that people try to keep their cholesterol level below 200. For a random sample of n = 30 control patients, the sample mean cholesterol was x¯ = 193.13 and the sample standard deviation was s = 22.30. Carry out the four following steps to test the appropriate hypothesis using α = 0.05.

(a) (2 points) State your hypotheses in words and using proper mathematical symbols and notation.

(b) (4 points) Compute your test statistic and state the degrees of freedom. Round your test statistic to two decimal places.

(c) (3 points) Find an approximate p-value using one of the text tables. Alternatively report the exact p-value using software (in this case indicate what software you used).

(d) (2 points) State your conclusion in the context of the research question using α = 0.05.

Answer 1

Part a)

To Test :-

H0 :- µ = 200
H1 :- µ < 200

Part b)

Test Statistic :-
t = ( X̅ - µ ) / (S / √(n) )
t = ( 193.13 - 200 ) / ( 22.3 / √(30) )
t = -1.69

Degree of freedon = n - 1 = 29

Part c)

P - value = P ( t > 1.69 ) = 0.0511

Part d)

Reject null hypothesis if P value < α = 0.05 level of significance
P - value = 0.0511 > 0.05, hence we fail to reject null hypothesis
Conclusion :- Fail to reject null hypothesis

There is insufficient evidence to support the claim that people try to keep their cholesterol level below 200.